Mappings of Butson-type Hadamard matrices

Patric R.J. Östergård*, William T. Paavola

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)
73 Downloads (Pure)


A BH(q,n) Butson-type Hadamard matrix H is an n×n matrix over the complex qth roots of unity that fulfils HH=nIn. It is well known that a BH(4,n) matrix can be used to construct a BH(2,2n) matrix, that is, a real Hadamard matrix. This method is here generalised to construct a BH(q,pn) matrix from a BH(pq,n) matrix, where q has at most two distinct prime divisors, one of them being p. Moreover, an algorithm for finding the domain of the mapping from its codomain in the case p=q=2 is developed and used to classify the BH(4,16) matrices from a classification of the BH(2,32) matrices.

Original languageEnglish
Pages (from-to)2387-2397
Number of pages11
JournalDiscrete Mathematics
Issue number9
Publication statusPublished - 1 Sep 2018
MoE publication typeA1 Journal article-refereed


  • Butson-type Hadamard matrix
  • Classification
  • Complex matrix
  • Mapping
  • Monomial equivalence


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